Textbook Question
Multiply or divide as indicated.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 24
Evaluate each exponential expression: (-3)3 (-2)2
Verified step by step guidance1
Identify the expression to evaluate: \((-3)^3 \times (-2)^2\).
Evaluate each exponential term separately. For \((-3)^3\), raise -3 to the power of 3, which means multiplying -3 by itself three times: \((-3) \times (-3) \times (-3)\).
For \((-2)^2\), raise -2 to the power of 2, which means multiplying -2 by itself two times: \((-2) \times (-2)\).
Calculate the results of each exponential expression individually, keeping track of the signs carefully.
Multiply the two results obtained from the previous step to get the final value of the expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents and Powers
An exponent indicates how many times a base number is multiplied by itself. For example, a^n means multiplying 'a' by itself 'n' times. Understanding this helps in evaluating expressions like (-3)^3, which means (-3) × (-3) × (-3).
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Negative Bases with Exponents
When a negative number is raised to a power, the sign of the result depends on whether the exponent is even or odd. An odd exponent results in a negative product, while an even exponent results in a positive product. For instance, (-3)^3 is negative, but (-2)^2 is positive.
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Multiplication of Exponential Expressions
When multiplying exponential expressions with different bases, calculate each power separately first, then multiply the results. For example, evaluate (-3)^3 and (-2)^2 individually, then multiply the two values to get the final answer.
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Related Practice
Textbook Question
Find the intersection of the sets. {s,e,t}∩{t,e,s}
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Textbook Question
Simplify each exponential expression in Exercises 23–64.
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Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0.
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In Exercises 17–38, factor each trinomial, or state that the trinomial is prime. 2x^2+5x−3
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Simplify each exponential expression in Exercises 23–64. x−2y